Non equilibrium current fluctuations in stochastic lattice gases

TL;DR

This paper investigates the probability and nature of current fluctuations in stochastic lattice gases, establishing a large deviation principle and exploring dynamical phase transitions and fluctuation relations.

Contribution

It extends the dynamic approach for density fluctuations to current fluctuations, deriving a large deviation principle and analyzing dynamical phase transitions.

Findings

Established a large deviation principle for empirical current fluctuations.

Identified scenarios of dynamical phase transitions in specific models.

Derived a fluctuation relation similar to Gallavotti-Cohen theorem.

Abstract

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation $j$ of the empirical current with a rate functional $\mc I (j)$. We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional $\mc I $. We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of $\mc I$ and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.